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Logic
A:
B:
A:
B:
A:
B:
Capital punishment is immoral.
No it isn’t!
Yes it is!
Well, what do you know about it?
I know more about it then you do!
Oh yeah? You’re an idiot!
Basic Terms
Logic: the study of how to reason well.
Argument: an attempt to show that something is true by providing
evidence…the connection by which the conclusion is said “to follow” from
the premise is called inference…
2 types of arguments: deductive and inductive reasoning
Deductive: reasons from the whole to the part…universal to the particular
Inductive: reasons from the part to the whole…particular to the universal
Syllogism: the most traditional and most common form of a deductive
argument consisting of 2 premises and a concluding statement…Greek
meaning propositions considered together…a valid argument form…there
are 2 different types of syllogisms that we will look at…
The categorical syllogism: A complete sentence, with one subject
and one predicate, that is either valid or invalid (needs reasoning).
The conditional syllogism: an argument that involves a precursor
and a consequent signalled by the words “if…then”
Validity: Valid thinking is thinking in conformity with the rules. If
the premises are true and the reasoning is valid, then the conclusion
will be valid out of a force of necessity.
Non-sequitur: (it does not follow). This means that the conclusion
cannot be deduced with certitude from the given premises. An
invalid argument.
The Subject: that about which something is said.
All giraffes are animals. (giraffes = subject)
The Predicate: that which is said about something.
All giraffes are animals. (animals = predicate)
The copula: connects together or separates the S and
the P. This term can hidden in the premise but can
always be inserted back in to separate the S and P.
All giraffes are animals. (is/is not)
All monkeys climb. (hidden copula)
All monkeys are animals that climb.
First, we look at categorical syllogism…then we
will move on to conditional or hypothetical
syllogisms next week…
For Example:
It is immoral to kill people.
Capital punishment is the killing of persons.
Therefore, capital punishment is immoral.
What is the subject?
What is the predicate?
The four Standard Propositional Codes for premises and
concluding statements.
These codes come from the Latin words "Affirmo" and
"Nego".
Affirmo: I affirm. Note the A and the I
Nego: I deny. Note the E and the O
A - universal affirmative: All S is P
I - particular affirmative: Some S is P
O - particular negative: Some S is not P.
E - universal negative: No S is P.
The parts of a categorical syllogism:
a. The two premises.
All A is B (first premise)
Some B is C (second premise)
Therefore, Some C is A
b. The Conclusion.
In the above syllogism, Therefore, Some C is A
The major term: this term is always the P (predicate) of the
conclusion. In the example directly above, A is the major term.
The minor term: this term is always the S (subject) of the
conclusion. In the example directly above, C is the minor term.
The middle term: this term is never in the conclusion but appears
twice in the premises. (The function of the middle term is to
connect together or keep apart the S and P in the conclusion).
Distribution: This is a very important term in logic. A distributed
term covers 100% of the things referred to by the term.
An undistributed term covers less than 100% of the things referred
to by the term (few, many, almost all).
For instance, All men are mortal. - and - Some men are Italian.
In this statement, "men" is distributed; for it covers 100% of the
things referred by the term "men".
“Mortal” is undistributed. Why?
Because women can be mortal.
In Some men are Italian, "men" is undistributed; for the term
covers less than 100% of the things referred to by the term "men".
“Italian” in undistributed. Why?
Because women can Italian as well.
Universal Affirmative statements (A statements): the subject is
distributed, the predicate is undistributed.
Universal Negative statements (E statements): both the subject and
the predicate are distributed.
Particular Affirmative statements (I statements): neither subject nor
predicate is distributed (both are undistributed).
Particular Negative statements (O statements): the predicate alone
is distributed.
Note the following (bold and underline = distributed)…the
terms that are not underlined is undistributed…
A = All S is P
I = Some S is P
E = No S is P
O = Some S is not P
Rules of Syllogistic (categorical) reasoning.
1. In a valid categorical syllogism, the middle term must be
distributed at least once.
2. In a valid categorical syllogism, any term which is distributed in
the conclusion must also be distributed in the premises.
3. A syllogism must have three and only three terms.
Rules of Syllogistic (categorical) reasoning continued
4. From two negative premises, no conclusion can be drawn.
5. If a premise is particular, the conclusion must be particular.
6. If a premise is negative, the conclusion must be negative.
Examples of violations
From two negative premises, no conclusion can be drawn.
• No dogs are cows
• No cows are pigs
• Therefore, no dogs are pigs.
If a premise is particular, the conclusion must be particular.
• Some Italians are from Calabria.
• All Italians love spaghetti
• Therefore, all those from Calabria love spaghetti.
In a valid categorical syllogism, the middle term must be
distributed at least once.
• All Germans love beer
• All Irishmen love beer
• Therefore, all Irishmen are Germans.
In a valid categorical syllogism, any term which is distributed
in the conclusion must also be distributed in the premises.
• All principals know about administrative problems
• No secretary is a principal.
• Therefore, no secretary knows about administrative problems
A syllogism must have three and only three terms.
• All Canadians like hockey.
• All Italians like soccer.
• Therefore, some Canadians like soccer.
If a premise is particular, the conclusion must be particular.
Some men are American
All Americans love apple pie
Therefore, all men love apple pie.
Again, if a premise is particular, the conclusion must be particular.
• Some men are Canadian.
• All Canadians love hockey.
• Therefore, all men love hockey.
If a premise is negative, the conclusion must be negative.
• Some Canadians are not hockey players.
• Some hockey players are professionals
• Therefore, some professionals are Canadian.
Steps to Take
in order to determine the validity of a syllogism
1. Circle your middle term.
2. Determine what kind of statement is the first
premise (I.e., A statement, E statement, etc.)
3. Determine what kind of statement is the second
premise. (I.e., A statement, E statement, etc.)
4. Determine what kind of statement is the conclusion. (I.e., A
statement, E statement, etc.)
5. Place a “d” above all your distributed terms
6. Check to see if your middle term is distributed at least
once. If it is, move on to #7.
7. Check your major and minor terms in the conclusion. If
one of them is distributed, see if that term is distributed in
the premises.
8. Check to see if any other rule is violated. If not, you
have a valid syllogism.
A note on deductive logic…
Watson and Holmes are out on a camping trip. In the
middle of the night Holmes wakes up Watson and
asks, “Watson, look up into the sky and tell me what
you see.”
“I see millions of stars, Holmes.” says Watson.
“…and what do you conclude from that, Watson” says
Holmes.
Watson thinks for a moment. “Well” he says to Holmes.
“…Astronomically, it tells me that there are millions of
galaxies an potentially billions of planets.
Astrologically, I observe that Saturn is in Leo.
Horologically, I deduce that the time is about a
quarter past three. Meteorologically, I suspect that
we will have a beautiful day tomorrow. Theologically,
I see that God is all powerful, and we are small and
insignificant. Uh, what does it tell you Holmes?”
Holmes replies…“Someone has stolen our tent, Watson”